In a house of any size it is easy to get sufficient oxygen for breathing. If a combustion furnace is not operating you could live for days on the oxygen in your house with no fresh air at all. What we often mistake for a lack of oxygen is a concentration of pollutants. Carbon dioxide (CO2) for example, is something that we create ourselves in the process of breathing. Too high a concentration of CO2 and we begin to complain that we need fresh air. We're not lacking oxygen; we've got too much carbon dioxide.
If the air is cleaned (by any of a number of fancy air cleaners) without adding fresh air, you could be lacking oxygen. If air pollutants are kept under control by controlled ventilation there will be plenty of oxygen for both you